Energy Stable L2 Schemes for Time-Fractional Phase-Field Equations

DOI10.1016/J.JCP.2022.111085arXiv2108.08437MaRDI QIDQ6375555

Chaoyu Quan, Author name not available (Why is that?)

Publication date: 18 August 2021

Abstract: In this article, the energy stability of two high-order L2 schemes for time-fractional phase-field equations is established. We propose a reformulation of the L2 operator and also some new properties on it. We prove the energy boundedness (by initial energy) of an L2 scalar auxiliary variable scheme for any phase-field equation and the fractional energy law of an implicit-explicit L2 Adams--Bashforth scheme for the Allen--Cahn equation. The stability analysis is based on a new Cholesky decomposition proposed recently by some of us.

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11)

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